Context. Gaia Data Release 1 allows the recalibration of standard candles such as the red clump stars. To use those stars, they first need to be accurately characterised. In particular, colours are needed to derive interstellar extinction. As no filter is available for the first Gaia data release and to avoid the atmosphere model mismatch, an empirical calibration is unavoidable. Aims. The purpose of this work is to provide the first complete and robust photometric empirical calibration of the Gaia red clump stars of the solar neighbourhood through colour–colour, effective temperature–colour, and absolute magnitude–colour relations from the Gaia, Johnson, 2MASS, Hipparcos, Tycho-2, APASS-SLOAN, and WISE photometric systems, and the APOGEE DR13 spectroscopic temperatures. Methods. We used a 3D extinction map to select low reddening red giants. To calibrate the colour–colour and the effective temperature–colour relations, we developed a MCMC method that accounts for all variable uncertainties and selects the best model for each photometric relation. We estimated the red clump absolute magnitude through the mode of a kernel-based distribution function. Results. We provide 20 colour versus G−K_s relations and the first T_eff versus G−K_s calibration. We obtained the red clump absolute magnitudes for 15 photometric bands with, in particular, M_Ks = (−1.606 ± 0.009) and M_G = (0.495 ± 0.009) + (1.121 ± 0.128)(G−K_s−2.1). We present a dereddened Gaia-TGAS HR diagram and use the calibrations to compare its red clump and its red giant branch bump with Padova isochrones.